Covariance expressions for second and lower order derivatives of the anomalous potential

The University Archives has determined that this item is of continuing value to OSU's history.Auto- and cross-covariance expressions for the anomalous potential of the Earth and its first and second order derivatives are derived based on three different degree-variance models. A Fortran IV subroutine is listed and documented that may be used for the computation of auto- and cross-covariance between any of the following quantities: (1) the anomalous potential (T), (2) the negative gravity disturbance/r, (3) the gravity anomaly Δg, (5) the second order radial derivative of T, (6), (7) the latitude and longitude components of the deflection of the vertical, (8), (9) the derivatives of northern and eastern direction of Δg, (10), (11) the derivatives of the gravity disturbance in northern and eastern direction, (12) – (14) the second order derivatives of T in northern, in mixed northern and eastern and in eastern direction. Values of different kinds of covariance of second order derivatives for varying spherical distance and height are tabulated.Danish Geodetic InstituteU.S. Air Force Contract no. F19628-TR-C-0010Ohio State Research Foundation Project no. 4214B

Comparisons of global topographic/isostatic models to the Earth's observed gravity field

The Earth's gravitational potential, as described by a spherical harmonic expansion to degree 180, was compared to the potential implied by the topography and its isostatic compensation using five different hypothesis. Initially, series expressions for the Airy/Heiskanen topographic isostatic model were developed to the third order in terms of (h/R), where h is equivalent rock topography and R is a mean Earth radius. Using actual topographic developments for the Earth, it was found that the second and third terms of the expansion contributed 30 and 3 percents, of the first of the expansion. With these new equations it is possible to compute depths (D) of compensation, by degree, using 3 different criteria. The results show that the average depth implied by criterion I is 60 km while it is about 33 km for criteria 2 and 3 with smaller compensation depths at the higher degrees. Another model examined was related to the Vening-Meinesz regional hypothesis implemented in the spectral domain. Finally, oceanic and continental response functions were derived for the global data sets and comparisons made to locally determined values

Non-stationary covariance function modelling in 2D least-squares collocation

Standard least-squares collocation (LSC) assumes 2D stationarity and 3D isotropy, and relies on a covariance function to account for spatial dependence in the ob-served data. However, the assumption that the spatial dependence is constant through-out the region of interest may sometimes be violated. Assuming a stationary covariance structure can result in over-smoothing of, e.g., the gravity field in mountains and under-smoothing in great plains. We introduce the kernel convolution method from spatial statistics for non-stationary covariance structures, and demonstrate its advantage fordealing with non-stationarity in geodetic data. We then compared stationary and non-stationary covariance functions in 2D LSC to the empirical example of gravity anomaly interpolation near the Darling Fault, Western Australia, where the field is anisotropic and non-stationary. The results with non-stationary covariance functions are better than standard LSC in terms of formal errors and cross-validation against data not used in the interpolation, demonstrating that the use of non-stationary covariance functions can improve upon standard (stationary) LSC

Error sources and data limitations for the prediction ofsurface gravity: a case study using benchmarks

Gravity-based heights require gravity values at levelled benchmarks (BMs), whichsometimes have to be predicted from surrounding observations. We use EGM2008 andthe Australian National Gravity Database (ANGD) as examples of model and terrestrialobserved data respectively to predict gravity at Australian national levelling network(ANLN) BMs. The aim is to quantify errors that may propagate into the predicted BMgravity values and then into gravimetric height corrections (HCs). Our results indicatethat an approximate ±1 arc-minute horizontal position error of the BMs causesmaximum errors in EGM2008 BM gravity of ~ 22 mGal (~55 mm in the HC at ~2200 melevation) and ~18 mGal for ANGD BM gravity because the values are not computed atthe true location of the BM. We use RTM (residual terrain modelling) techniques toshow that ~50% of EGM2008 BM gravity error in a moderately mountainous regioncan be accounted for by signal omission. Non-representative sampling of ANGDgravity in this region may cause errors of up to 50 mGals (~120 mm for the Helmertorthometric correction at ~2200 m elevation). For modelled gravity at BMs to beviable, levelling networks need horizontal BM positions accurate to a few metres, whileRTM techniques can be used to reduce signal omission error. Unrepresentative gravitysampling in mountains can be remedied by denser and more representative re-surveys,and/or gravity can be forward modelled into regions of sparser gravity

High-resolution regional gravity field recovery from Poisson wavelets using heterogeneous observational techniques

2016-2017 > Academic research: refereed > Publication in refereed journal201804_a bcmaVersion of RecordPublishe